Maple worksheets on the Duffing equation |

Numerical methods topics:

- Introduction - errors
- Root-finding
- Interpolation
- Numerical integration
- 1st order differential equations
- 2nd order differential equations
- Linear systems
- Finite difference methods
- The Duffing equation
- Approximation of functions
- The numerical evaluation of mathematical functions
- Special inverse functions
- The derivation of Runge-Kutta schemes
- Interpolation for Runge-Kutta schemes

The following Maple worksheets can be downloaded.

They are all compatible with

Classic Worksheet Maple 10.

Introduction and free oscillations-duff1.mws

- The double-well oscillator and the Duffing equation
- The Duffing equation for free oscillations
- A periodic solution through both wells

Damped oscillations-duff2.mws

- The Duffing equation for damped oscillations
- A sample numerical solution
- The two basins of attraction in the phase plane
- Solutions attracted to each well

Forced and damped oscillations-duff3.mws

- The Duffing equation with both damping and forcing terms
- A non-chaotic solution
- The transition to chaos

Forced and damped oscillations (continued)-duff4.mws

- A periodic solution with period 4 times the period of the driving force
- Reconstructing the solution and its symmetrical counterpart
- Poincare sections